On Generalized Differences for Biospeckle Image Analysis

Biospeckle is a technique whose purpose is to observe and study the underlying activity of some material. The technique has its roots on optical physics, and its first step is an image acquisition process that produces a video sequence whose characteristics allow researchers to have an interpretation of the activity of the observed material by an analysis of the video content. The recent literature on this subject presents several different measurements for analyzing the video sequence. One of the most popular measurement is the Generalized Difference (GD). The computation of the GD has an asymptotic complexity of O(n2). In this paper we propose: i) an alternative O(n) algorithm for the computation of the GD, and ii) an alternative measurement, that we call GD*. We discuss the qualitative similarities between the GD and the GD*. We conclude that the GD* is an alternative generalized difference measurement, and thus it can replace the GD in many applications. We show that the GD* is a function of the variance, and it can be computed in O(n). Finally, if the GD itself is desired as measurement, it can now be computed in O(n) by the novel algorithm presented in this paper.